Problem: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}x-y &= 4 \\ -7x-8y &= 2\end{align*}$
Begin by moving the $x$ -term in the second equation to the right side of the equation. $-8y = 7x+2$ Divide both sides by $-8$ to isolate $y$ $y = {-\dfrac{7}{8}x - \dfrac{1}{4}}$ Substitute this expression for $y$ in the first equation. $x-({-\dfrac{7}{8}x - \dfrac{1}{4}}) = 4$ $x + \dfrac{7}{8}x + \dfrac{1}{4} = 4$ Simplify by combining terms, then solve for $x$ $\dfrac{15}{8}x + \dfrac{1}{4} = 4$ $\dfrac{15}{8}x = \dfrac{15}{4}$ $x = 2$ Substitute $2$ for $x$ back into the top equation. $ 2-y = 4$ $2-y = 4$ $-y = 2$ The solution is $\enspace x = 2, \enspace y = -2$.